What are the state-of-the-art meta-reinforcement learning methods?
One of the most recent papers on meta-RL is meta-Q-learning. This paper introduces Meta-Q-Learning (MQL), a new off-policy algorithm for meta-reinforcement learning (meta-RL). MQL builds upon three simple ideas.

Q-learning is competitive with state-of-the-art meta-RL algorithms if given access to a context variable that is a representation of the past trajectory.

Using a multi-task objective to maximize the average reward across the training tasks is an effective method to meta-train RL policies.

past data from the meta-training replay buffer can be recycled to adapt the policy on a new task using off-policy updates


Experiments on standard continuous-control benchmarks suggest that MQL compares favorably with state-of-the-art meta-RL algorithms.
I think that other references to other work on meta-RL are present in the experiments part of the MQL paper.